Moment operators of the Cartesian margins of the phase space observables

The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the $x$-margin are polynomials of the position operator and those of the $y$-margin are polynomials of the momentum operator.Comment: 14 page

Signal processing in local neuronal circuits based on activity-dependent noise and competition

We study the characteristics of weak signal detection by a recurrent neuronal network with plastic synaptic coupling. It is shown that in the presence of an asynchronous component in synaptic transmission, the network acquires selectivity with respect to the frequency of weak periodic stimuli. For non-periodic frequency-modulated stimuli, the response is quantified by the mutual information between input (signal) and output (network's activity), and is optimized by synaptic depression. Introducing correlations in signal structure resulted in the decrease of input-output mutual information. Our results suggest that in neural systems with plastic connectivity, information is not merely carried passively by the signal; rather, the information content of the signal itself might determine the mode of its processing by a local neuronal circuit.Comment: 15 pages, 4 pages, in press for "Chaos

Semispectral measures as convolutions and their moment operators

The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are then applied to conveniently determine the moment operators of the Cartesian margins of the phase space observables.Comment: 7 page

Chaotic Phase Synchronization in Bursting-neuron Models Driven by a Weak Periodic Force

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1 : 1 phase locking between a single spike and one period of the force and 1 : l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale

Fermi Large Area Telescope Observations of the Cosmic-Ray Induced gamma-ray Emission of the Earth's Atmosphere

We report on measurements of the cosmic-ray induced gamma-ray emission of Earth's atmosphere by the Large Area Telescope onboard the Fermi Gamma-ray Space Telescope. The LAT has observed the Earth during its commissioning phase and with a dedicated Earth-limb following observation in September 2008. These measurements yielded 6.4 x 10^6 photons with energies >100MeV and ~250hours total livetime for the highest quality data selection. This allows the study of the spatial and spectral distributions of these photons with unprecedented detail. The spectrum of the emission - often referred to as Earth albedo gamma-ray emission - has a power-law shape up to 500 GeV with spectral index Gamma = 2.79+-0.06.Comment: Accepted for publication in PR

Fermi-LAT Study of Gamma-ray Emission in the Direction of Supernova Remnant W49B

We present an analysis of the gamma-ray data obtained with the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope in the direction of SNR W49B (G43.3-0.2). A bright unresolved gamma-ray source detected at a significance of 38 sigma is found to coincide with SNR W49B. The energy spectrum in the 0.2-200 GeV range gradually steepens toward high energies. The luminosity is estimated to be 1.5x10^{36} (D/8 kpc)^2 erg s^-1 in this energy range. There is no indication that the gamma-ray emission comes from a pulsar. Assuming that the SNR shell is the site of gamma-ray production, the observed spectrum can be explained either by the decay of neutral pi mesons produced through the proton-proton collisions or by electron bremsstrahlung. The calculated energy density of relativistic particles responsible for the LAT flux is estimated to be remarkably large, U_{e,p}>10^4 eV cm^-3, for either gamma-ray production mechanism.Comment: 9 pages, 10 figure

Fermi-LAT observations of the exceptional gamma-ray outbursts of 3C 273 in September 2009

We present the light curves and spectral data of two exceptionally luminous gamma-ray outburts observed by the Large Area Telescope (LAT) experiment on board Fermi Gamma-ray Space Telescope from 3C 273 in September 2009. During these flares, having a duration of a few days, the source reached its highest gamma-ray flux ever measured. This allowed us to study in some details their spectral and temporal structures. The rise and decay are asymmetric on timescales of 6 hours, and the spectral index was significantly harder during the flares than during the preceding 11 months. We also found that short, very intense flares put out the same time-integrated energy as long, less intense flares like that observed in August 2009.Comment: Corresponding authors: E. Massaro, [email protected]; G. Tosti, [email protected]. 15 pages, 4 figures, published in The Astrophysical Journal Letters, Volume 714, Issue 1, pp. L73-L78 (2010

Fermi Large Area Telescope Observations of Misaligned AGN

Analysis is presented on 15 months of data taken with the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope for 11 non-blazar AGNs, including 7 FRI radio galaxies and 4 FRII radio sources consisting of 2 FRII radio galaxies and 2 steep spectrum radio quasars. The broad line FRI radio galaxy 3C 120 is reported here as a gamma-ray source for the first time. The analysis is based on directional associations of LAT sources with radio sources in the 3CR, 3CRR and MS4 (collectively referred to as 3C-MS) catalogs. Seven of the eleven LAT sources associated with 3C-MS radio sources have spectral indices larger than 2.3 and, except for the FRI radio galaxy NGC 1275 that shows possible spectral curvature, are well described by a power law. No evidence for time variability is found for any sources other than NGC 1275. The gamma-ray luminosities of FRI radio galaxies are significantly smaller than those of BL Lac objects detected by the LAT, whereas the gamma-ray luminosities of FRII sources are quite similar to those of FSRQs, which could reflect different beaming factors for the gamma-ray emission. A core dominance study of the 3CRR sample indicate that sources closer to the jet axis are preferentially detected with the Fermi-LAT, insofar as the gamma-ray--detected misaligned AGNs have larger core dominance at a given average radio flux. The results are discussed in view of the AGN unification scenario.Comment: 28 pages, 8 figures, 2 tables. Accepted for publication in The Astrophysical Journa

Fermi LAT observations of cosmic-ray electrons from 7 GeV to 1 TeV

We present the results of our analysis of cosmic-ray electrons using about 8 million electron candidates detected in the first 12 months on-orbit by the Fermi Large Area Telescope. This work extends our previously-published cosmic-ray electron spectrum down to 7 GeV, giving a spectral range of approximately 2.5 decades up to 1 TeV. We describe in detail the analysis and its validation using beam-test and on-orbit data. In addition, we describe the spectrum measured via a subset of events selected for the best energy resolution as a cross-check on the measurement using the full event sample. Our electron spectrum can be described with a power law $\propto {\rm E}^{-3.08 \pm 0.05}$ with no prominent spectral features within systematic uncertainties. Within the limits of our uncertainties, we can accommodate a slight spectral hardening at around 100 GeV and a slight softening above 500 GeV.Comment: 20 pages, 23 figures, 2 tables, published in Physical Review D 82, 092004 (2010) - contact authors: C. Sgro', A. Moisee

Fermi Gamma-ray Space Telescope Observations of Recent Gamma-ray Outbursts from 3C 454.3

The flat spectrum radio quasar 3C~454.3 underwent an extraordinary outburst in December 2009 when it became the brightest gamma-ray source in the sky for over one week. Its daily flux measured with the Fermi Large Area Telescope at photon energies E>100 MeV reached F = 22+/-1 x 10^-6 ph cm^-2 s^-1, representing the highest daily flux of any blazar ever recorded in high-energy gamma-rays. It again became the brightest source in the sky in 2010 April, triggering a pointed-mode observation by Fermi. The correlated gamma-ray temporal and spectral properties during these exceptional events are presented and discussed. The main results show flux variability over time scales less than 3 h and very mild spectral variability with an indication of gradual hardening preceding major flares. No consistent loop pattern emerged in the gamma-ray spectral index vs flux plane. A minimum Doppler factor of ~ 15 is derived, and the maximum energy of a photon from 3C 454.3 is ~ 20 GeV. The spectral break at a few GeV is inconsistent with Klein-Nishina softening from power-law electrons scattering Ly_alpha line radiation, and a break in the underlying electron spectrum in blazar leptonic models is implied.Comment: submitted to the Astrophysical Journa